In order to provide a proper color match to a target sample that is coated with a target coating using formulation or search engines (or a visual process), it is desirable to determine the correct pigmentation of the target coating. If the same pigments or appropriate offsets as those in the target coating are utilized, a formulation or search process may arrive at an apparent optimum solution as to the formulation of the target coating. On the other hand, excluding those pigments, either deliberately or inadvertently, from availability will result in a less than optimal color match.
Several existing formulation engines and methodologies attempt to encompass pigment selection and formulation via various algorithms. Various pigment identification packages and formulation engines take a “brute” force, guess and check type of approach to provide formulations and pigment information to their users. The combinatorial approach, or brute force method, is a frequently used method in which nearly all available pigments are combined in all combinations available given an end number of pigments desired in the final match. The combinatorial approach may utilize the Kubelka-Munk equation or a derivative thereof to generate the various formulations. Although there have been some methods which restrict the usage of some pigments given certain conditions to optimize the engine's speed, the end result is that the formula combinations are validated against the sample and a selection of one or more formulas most nearly matching the target coating are provided to the user. There are various forms of Delta E's or other colorimetric assessment algorithms that are used to determine the accuracy of the match compared to the sample.
Other solutions require the user to submit a sample set of toners to a formulation engine, and still other methods select a predefined subset of toners to use. Neither of these approaches utilizes a stepwise method and thus often results in non-optimal solutions. These methods have been typically burdensome for users and lack proper “intuition” to provide a streamlined method to a good solution for the user. Additionally, by the nature of such methodology, appropriate pigments necessary to match the target coating may be excluded.
Neural networks have been used to select color matches from existing databases of pre-generated possible matches or to act as formulation engines themselves. The strength of a neural network is its ability to address both linear and non-linear relationships, but this strength comes at a cost of bulkiness, inflexibility, and a requirement of significant overhead to meticulously manage a sometimes large learning database and structure. The inflexibility, or rigid operation, of a neural network generally must be used in a feedback design to optimize the node weightings leading to and within the hidden layers of the network. A neural network requires this type of backpropagation of errors acquired from desired outputs in order to “learn.” The actual learning, or training, of the neural network is based on the reduction of the calculated error given a desired output by repeated reintroduction of the input and adjustment of the weights based on the prior iteration's error.
As can be seen in FIG. 1, a typical neural network requires a nearly ideally defined input and requires significant effort to update and/or alter the various layers (nodes) if an error needs to be corrected or a new piece of information needs to be considered. Although fewer steps, compared to some prior models, are apparent to the user, a neural network tends to be relatively slow and unidirectional due to its nature of trying to encompass the resolution to a formulation or color search in one massive step. Also, as with the methodologies discussed hereinabove, the exclusion of necessary pigments is a possibility. A neural network also requires precise and somewhat tedious maintenance of the weights, the database, the calculations, the sophisticated and rigid process mapping, and the substantial “training” to be effective.
Thus, there is a need for systems and methods that have flexibility to partition the processing steps into smaller multidirectional pieces and that utilize a feed forward type of design for speed and accuracy. There is also a need for systems and methods that minimize user interaction and create a flexible stepwise methodology of pigment identification and tolerancing in combination with a formulation engine.